What is the area of a triangle with vertices at (5,0), (-3,1) and (2,6)?



6 units squared


54 units squared


22. 5 units squared


36. 5 units squared

Answer:

  8

Step-by-step explanation:

The length of the top segment is the difference of its x-coordinates: 7-2=5.

The length of the bottom segment is the difference of its x-coordinates: 9-(-2)=11.

The length of the midsegment is the average of the lengths of the top and bottom segments:

  (5 +11)/2 = 16/2 = 8

The length of the midsegment is 8.

_____

Additional comment

You can check this by drawing a midline at y = 1.5. It intersects AD on the y-axis (x=0), and intersects BC at x=8. The length of the midline is the difference of those x-coordinates: 8-0 = 8.

Answer:

It’s right!

Step-by-step explanation:

The differentiation of the function is f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

from the question, we have the following parameters that can be used in our computation:

f(x) = 2x³ + 6x - 1/x + 3eˣ - sin(x)

The derivative of the functions can be calculated using the first principle which states that

if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹

Using the above as a guide, we have the following:

f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

Hence, the differentiation of the function is f'(x) = 6x² + 6 - ln(x) + 3eˣ - cos(x)

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Answer: HI = 5.3 cm

Let HI = x

GH = 2cm

m< H = 68 degrees

to find HI, we will need to apply the SOH CAH TOA RULE

HI = hypotenus

GH = adjacent

Cos 68 = adjacent / hypotenus

Cos 68 = 2 / x

Cross multiply

2 = x * cos 68

cos 68 = 0.3746

2 = x * 0.3746

Isolate x

x = 2/0.3746

x = 5.3cm

Therefore, HI is 5.3cm

Answer:

Step-by-step explanation:

Area of front and back faces:

Area of top and bottom faces:

Area of left and right faces:

Total surface area:

Answer:

256 \(in^{2} \)

Step-by-step explanation:

It is the frame thickness in inches that would result in a picture with 100 square inches of surface area and one side length of 2x + 8 and the other side length of 2x +10.  

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

The picture is 100 square inches in total area,

The width is 8+2x,

The length is 10+2x,

The solution to the equation will give the value of x = the thickness of the frame =

100= (8+2x)(10+2x)

= 80 +36x + 4x²

4x² + 36x -20=0

x² + 9x -5 = 0

x² + 9x + 81/4 - 5 - 81/4 = 0

(x+9/2)² = 101/4

x+9/2 = √(101/4) = √25 = 5

x = -4 1/2 + 5 = 1/2-inch frame or slightly bigger than 1/2

8-inch width + 2(1/2) inch frame = 9 inches

10-inch length + 2(1/2) inch frame = 11 inches

9x11 = 99 ≈ 100 square inch area

x = slightly more than 1/2 inches

√(101/4) = 5.025 making x = 5.025-4.5 = 0.475 inches, slightly less than 1/2 inch

Hence, it is the frame thickness in inches that would result in a picture with 100 square inches of surface area and one side length of 2x + 8 and the other side length of 2x +10.  

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Answer:

B

Step-by-step explanation:

Answer:

B. -1/2

Step-by-step explanation:

See picture

Answer:

5^2 x^3 y

Step-by-step explanation:

Whatever the amount let's say there are four 3's the amount of that number goes to the top right, but the number stays the same 3^4

Hopefully this helps :)

We can learn a lot about a population if we select a sample of it.

Selecting a representative sample is an important aspect of conducting research or making inferences about a population. Here's more information about the concept of a representative sample and its significance:

Definition: A representative sample is a subset of individuals or elements from a larger population that accurately reflects the characteristics, diversity, and distribution of the population. The goal is to obtain a sample that closely resembles the population in terms of relevant attributes or variables of interest.

Random sampling: The most common approach to achieving a representative sample is through random sampling. Random sampling involves randomly selecting individuals or elements from the population, ensuring that each member of the population has an equal chance of being included in the sample. This helps minimize bias and increase the likelihood of obtaining a representative sample.

Importance of representativeness: A representative sample is crucial because it allows researchers to generalize their findings from the sample to the larger population. When the sample is representative, the results obtained from studying the sample are likely to be applicable and valid for the population as a whole.

Avoiding sampling bias: Sampling bias occurs when the selected sample is not representative of the population, leading to inaccurate or skewed results. Various types of bias, such as selection bias or non-response bias, can compromise the representativeness of the sample. Efforts must be made to minimize or address these biases to ensure the sample accurately represents the population.

Statistical validity: The validity of statistical inferences, such as estimating population parameters or testing hypotheses, relies on the representativeness of the sample. A representative sample helps ensure that the results obtained from the sample accurately reflect the characteristics and behavior of the larger population, increasing the statistical validity of the findings.

Generalizability: The ultimate goal of using a representative sample is to make valid inferences and generalizations about the population. By studying the sample, researchers can gain insights, make predictions, and draw conclusions that can be applied to the broader population with a certain level of confidence.

In summary, selecting a representative sample is vital for accurate research and drawing valid conclusions about a population. It helps minimize bias, ensures statistical validity, and allows for generalizing findings to the larger population with greater confidence.

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Answer:

Independent events - Random selection of  one

student - Selection of one boy to answer first question

Dependent Event - Selection of a girl student

Probability = 13.33 %

Step-by-step explanation:

The complete question is

Determine whether the scenario involves independent or dependent events. Then find the  probability

There are eight boys and eight girls in a

class. The teacher randomly selects one

student to answer a question. Later, the

teacher randomly selects a different student

to answer another question. The first

student is a boy and the second student is a

girl.

Solution

Independent events - Random selection of  one

student - Selection of one boy to answer first question

Dependent Event - Selection of a girl student

Probability

8C1 + 8C1/16C2

(8+8) /(8*15)

13.33 %

Answer:

$ 175

Step-by-step explanation:

Create an equation:

5000 = ax + 2900

a > 75

x = 12 months

5000 = 12a + 2900

12a = 2100

a = 175

Answer:

h_max = 12.56 units

(the exercise does no specify the units)

Step-by-step explanation:

You have the following function:

\(h(t)=-16t^2+6t+12\)    (1)

To calculate the maximum height reach by you, you first derivative the function h(t) respect to t:

\(\frac{dh(t)}{dt}=-32t+6\)

Next, you equal the result of the derivative to zero and you obtain t:

\(-32t+6=0\\\\t=\frac{6}{32}=\frac{3}{16}\)

Then, you replace this value of t in the equation (1) and you obtain the maximum height:

\(h(t)=-16(\frac{3}{16})^2+6(\frac{3}{16})+12\)

\(h(t)=12.56\)

hence, the maximum height is 12.56 units

For (x = 2), [y = (22 - 3x)] = 16, for (x = 4), [y = (22 - 3x)] = 10,

For (x = 5), [y = (22 - 3x)] = 7 and for (x = 6), [y = (22 - 3x)] = 4.

To solve this question, we simply have to substitute the value of "x" in the linear equation, all data provided in the question statement as well as the reference diagram, and for each value of "x", we will obtain a different value of "y" which will be our desired answers.

Given linear equation is  \(y = (22 - 3x)\).

So for (x = 2), \(y = [22 - (3*2)]=(22-6)=16\).

So for (x = 4), \(y = [22 - (3*4)]=(22-12)=10\).

So for (x = 5), \(y = [22 - (3*5)]=(22-15)=7\\\).

So for (x = 6), \(y = [22 - (3*6)]=(22-18)=4\).

hence, (x, y) = (2, 16), (4, 10O, (5, 7) and (6, 4).

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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The total area of the figure is obtained as option B: 21 3/8 cm².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

To find the total area of the figure, we need to find the area of the rectangle and the area of the triangle, then add them together.

The area of the rectangle is -

Length x Breadth

= (3 1/2) cm x (4 1/2) cm

= (7/2) cm x (9/2) cm

= 63/4 cm²

The area of the triangle is -

1/2 x Base x Height

= 1/2 x (4 1/2) cm x (5/2) cm

= 45/8 cm²

To find the total area of the figure, we add the area of the rectangle and the area of the triangle -

Total area = Area of rectangle + Area of triangle

Total area = (63/4) cm² + (45/8) cm²

Total area = (126/8) cm² + (45/8) cm²

Total area = 171/8 cm²

Therefore, the total area of the figure is 21 3/8 cm² or 21.375 cm² if we want to use decimal notation.

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Answer:

The GCF of 24 & 30 would be 6. The LCM of 24 & 30 would be 120.

Step-by-step explanation:

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the relative error in the surface area is approximately 0.005 or 0.5%.

To approximate the relative error in surface area when the edges of a 2x2x2 m² cube are mismeasured by 2 cm, we can use the formula for relative error.

The relative error (E) is given by:

E = (ΔA / A)

Where ΔA is the change in the surface area and A is the original surface area.

The surface area of a cube with edge length L is given by:

A = 6L²

Given that the edges of the cube are mismeasured by 2 cm, the change in the edge length (ΔL) is 0.02 m.

Using the formula for relative error, we have:

E = (ΔA / A) = (6ΔL / (6L²))

= (ΔL / L²)

Substituting the values, we get:

E = (0.02 / (\(2^2\)))

= 0.02 / 4

= 0.005

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Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

Answer:

Area = 6cm^2

Step-by-step explanation:

Pythagorean Theorem = \(a^{2} + b^{2} = c^{2}\)

\(a^{2} + 3^{2} = 5^{2}\)

or

\(a^{2} + 9 = 25\)

Subtract 9 from 25.

25 - 9 = 16

Square root 16 to get 4.

a = 4

Now to find the area.

Area = 1/2(3*4)

12/2 = 6

The area of the kite in the image given is determined as: 100 ft².

The area of a kite ca n be determined by calculating the product of its diagonals, then divide by 2.

Therefore, the formula for finding the area of a kite, whose diagonals lengths are q and p respectively is expressed as:

Area of kite = (p ×  q) / 2.

Given the image of a kite above, the length of each diagonals are:

p = 20 + 30 = 50 ft

q = 2 + 2 = 4 ft.

The area of the kite = (p ×  q) / 2 = (50 ×  4) / 2

The area of the kite = (200) / 2

= 100 ft².

Therefore, the kite has an area of 100 ft².

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Answer: 300

Step-by-step explanation:

60/100 multiplied by x = 180

Multiplying both sides by 100 and dividing both sides by 60,

we have x = 180 × 100/60

x = 300

Answer:

DF=2.68

Step-by-step explanation:

Given that the triangles, ABC and DEF are similar to each other, applying the theorem of similar triangles, the length of:

a. Segment DF = 2.68

b. Segment EF = 2.01

Recall the following about Triangles that are similar:

Thus:

Given that \(\triangle\)ABC and \(\triangle\)DEF are similar, therefore:

AB/DE = BC/EF = AC/DF

Length of Segment DF:

Using AB/DE = AC/DF,

AB = 2

AC = 4

DE = 1.34

DF = ?

\(\frac{2}{1.34} = \frac{4}{DF}\)

\(\frac{2}{1.34} = \frac{4}{DF}\\\\DF = \frac{4 \times 1.34}{2} \\\\\mathbf{DF = 2.68}\)

Length of Segment EF:

Using AB/DE = BC/EF,

AB = 2

BC = 3

DE = 1.34

EF = ?

\(\frac{2}{1.34} = \frac{3}{EF}\)

\(\frac{2}{1.34} = \frac{3}{EF}\\\\EF = \frac{3 \times 1.34}{2} \\\\\mathbf{EF = 2.01}\)

Therefore, given that the triangles, ABC and DEF are similar to each other, applying the theorem of similar triangles, the length of:

a. Segment DF = 2.68

b. Segment EF = 2.01

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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Write the highlighted digit's place and value.

3. 567; ones place                4. 6,327; thousandth place

5. 9,325; hundredth place    6. 8,281; tenth place

Write each number in standard form.

7. 5,000 + 500 + 3; 5,503     8. 2,000 + 300 + 20 + 9; 2,329

9. 4,000 + 600 + 8; 4,608     9. 9,000 + 300 + 70 + 2; 9,372

11. 1,221

We know Sierra has the same numbers in the thousandth and ones place, so keep does numbers: 1,?2?

It also has two more hundreds and 3 fewer ones place: Take the original number; 1,024 (Make sure you keep the numbers) into a equation; (1024+200)-3. First Add as it's in the ( ), then subtract, 1,221

I hope I've helped!

Answer:

#3. ones place. #4. thousands place.#5. hundreds place. #6. tens place. #7. 5,503. #8. 2,329. #9. 4,608. #10. 9,372.

Step-by-step explanation:

#11.sierras seat number 1,221

Answer: 2000

Step-by-step explanation: there are 1000 mililiters in every liter

Answer:

A: y = -4/5x + 3/2 i believe is the correct answer

Step-by-step explanation:

Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

The number 78.263 using ones, tenths, and thousandths means

This is the value of each digits based on its position in a number.

It is divided into whole number part and fractional part.

Whole number part:

Fractional part:

78.263

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The scale factor which takes circle m to circle n as depicted in the attached image is; 3.

It follows from the task content that the scale factor which takes circle m and transforms it to circle n is to be determined.

Hence, since both circles have the same center, the center can be taken as a point of reference.

Therefore, the distances between the center of the circles m and n to any point on their circumferences are; 3 units and 9 units respectively.

On this note, since circle n is; 9/3 = 3 times as large as circle m, it follows that the required scale factor is; 3.

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Answer:

if 160 is the whole investment over 8 years than 500

Step-by-step explanation:

Hope this helps

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